My research and investigations

This is a story about Finite Fields (有限域), or Galois Fields in honor of Évariste Galois (1811-1832).

This conversation is, of course, a fiction. Galois was barely 20 when he dies. Except for a few letters, manuscripts (some were lost) and published papers, there are not much written records from Galois, let alone conversations.

Galois is recognized as a math genius, during his lifetime and long after his death. However, his ideas are so far ahead of his time that his contemporaries could not understand his claims. Galois was not keen in organizing or explaining his thoughts, resulting in several frustrating episodes, ultimately leading to his early tragic death. It was not until 1843 that Joseph Liouville gave the first exposition of his remarkable ideas.

Conversation with a genius is always fascinating, even though this is imaginary. As the fire of youth subsides, he would have consolidated his ideas, and more willing to share his thoughts. While the talk is a fantasy, the contents – all the maths – are real good: logically true and with real applications.

By developing the theory of Finite Fields through chatting with Galois, his genius will be recognized, and the beauty of the theory will shine through.

In the conversation, G is Évariste Galois. X is the Unknown student (you and me), Y is his roommate, studying computer science, and Z is his Chinese friend. Other characters will pop in and out, from time to time. They meet on the Internet, at a place where all sorts of information can readily be found. The popular site, with a big logo G, is depicted as a bar, owned by Al, the Al-GBar.

Here is the talk.

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